Both bodies move; the heavier one moves less, but it doesn’t stay perfectly fixed.
Changing separation affects the period strongly (in this simplified circular model).
Model notes$\mathrm{AU}$ / $\mathrm{yr}$ / $M_{\odot}$
We assume perfectly circular orbits and point masses (no size, no tides, no relativity).
Units: distance in $\mathrm{AU}$, time in $\mathrm{yr}$, and masses in $M_{\odot}$. We use the teaching normalization
$$G = 4\pi^2\,\frac{\mathrm{AU}^3}{\mathrm{yr}^2\,M_{\odot}}.$$
In this instrument we take $m_1 = 1\,M_{\odot}$ and set $m_2$ via the mass-ratio slider, so
$$P^2 = \frac{a^3}{M_1 + M_2}$$
in this circular Keplerian model.
This is a visualization aid, not a full N-body integrator or a measured astrophysical binary.